Finite Group Databasebeta

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C₃×C₈×C₅₇₇ #72192080

order	13848
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₉×C₆₄ (order 4608) · Inn(G) = C₁ · Out(G) = C₂³×C₉×C₆₄
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₃₈₄₈
abelian	C₃×C₈×C₅₇₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃×C₅₇₇
socle, prime radical	C₂×C₃×C₅₇₇	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13848 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₃₈₄₈, D₂₇₆₉₆
Fitting subgroup of	D₁₃₈₄₈, Dic₆₉₂₄
maximal subgroup of	C₃×C₁₆×C₅₇₇, C₂×C₃×C₈×C₅₇₇, D₁₃₈₄₈, …
maximal normal subgroup of	C₃×C₁₆×C₅₇₇, C₂×C₃×C₈×C₅₇₇, D₁₃₈₄₈, …
maximal quotient of	C₃×C₁₆×C₅₇₇, C₂×C₃×C₈×C₅₇₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.